Classification of string links up to self delta-moves and concordance

Akira Yasuhara

doi:10.2140/agt.2009.9.265

Classification of string links up to self delta-moves and concordance

Akira Yasuhara^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

For an n-component string link, the Milnor's concordance invariant is defined for each sequence I = i₁i₂...i_m(i_j,in {1,...,n}) Let r(I) denote the maximum number of times that any index appears. We show that two string links are equivalent up to self Δ-moves and concordance if and only if their Milnor invariants coincide for all sequences I with r(I) ≤ 2.

Original language	English
Pages (from-to)	265-275
Number of pages	11
Journal	Algebraic and Geometric Topology
Volume	9
Issue number	1
DOIs	https://doi.org/10.2140/agt.2009.9.265
Publication status	Published - 2009
Externally published	Yes

Keywords

Concordance
Link-homotopy
Milnor invariant
Self Δ-equivalence
Self Δ-move
String link
Δ-move

ASJC Scopus subject areas

Geometry and Topology

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10.2140/agt.2009.9.265

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AB - For an n-component string link, the Milnor's concordance invariant is defined for each sequence I = i1i2...im(ij,in {1,...,n}) Let r(I) denote the maximum number of times that any index appears. We show that two string links are equivalent up to self Δ-moves and concordance if and only if their Milnor invariants coincide for all sequences I with r(I) ≤ 2.

KW - Concordance

KW - Link-homotopy

KW - Milnor invariant

KW - Self Δ-equivalence

KW - Self Δ-move

KW - String link

KW - Δ-move

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Classification of string links up to self delta-moves and concordance

Abstract

Keywords

ASJC Scopus subject areas

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